# A Sparsity Algorithm with Applications to Corporate Credit Rating

arXiv: https://arxiv.org/abs/2107.10306 · HTML: https://mlsanity.com/paper/2107.10306/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 47 references that are in the map.
- First posted on arXiv 21 Jul 2021.

## Builds on (most cited first, 12 of 12)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [European Union regulations on algorithmic decision-making and a "right to explanation"](https://mlsanity.com/paper/1606.08813/) (2016)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Reducing Sentiment Bias in Language Models via Counterfactual Evaluation](https://mlsanity.com/paper/1911.03064/) (2019)
- [Model Agnostic Supervised Local Explanations](https://mlsanity.com/paper/1807.02910/) (2018)
- [On Loss Functions for Deep Neural Networks in Classification](https://mlsanity.com/paper/1702.05659/) (2017)
- [Interpretable Credit Application Predictions With Counterfactual Explanations](https://mlsanity.com/paper/1811.05245/) (2018)
- [Sparse Regularization via Convex Analysis](https://mlsanity.com/paper/1803.06765/) (2018)
- [Application of Deep Neural Networks to assess corporate Credit Rating](https://mlsanity.com/paper/2003.02334/) (2020)
- [A comparative study of forecasting Corporate Credit Ratings using Neural Networks, Support Vector Machines, and Decision Trees](https://mlsanity.com/paper/2007.06617/) (2020)
- [Is Image Encoding Beneficial for Deep Learning in Finance? An Analysis of Image Encoding Methods for the Application of Convolutional Neural Networks in Finance](https://mlsanity.com/paper/2010.08698/) (2020)
- [Sparsity Constrained Minimization via Mathematical Programming with Equilibrium Constraints](https://mlsanity.com/paper/1608.04430/) (2016)

## Built on by (most cited first, 1 of 1)

- [Corporate Credit Rating: A Survey](https://mlsanity.com/paper/2309.14349/) (2023)

## Abstract (arXiv)

In Artificial Intelligence, interpreting the results of a Machine Learning technique often termed as a black box is a difficult task. A counterfactual explanation of a particular "black box" attempts to find the smallest change to the input values that modifies the prediction to a particular output, other than the original one. In this work we formulate the problem of finding a counterfactual explanation as an optimization problem. We propose a new "sparsity algorithm" which solves the optimization problem, while also maximizing the sparsity of the counterfactual explanation. We apply the sparsity algorithm to provide a simple suggestion to publicly traded companies in order to improve their credit ratings. We validate the sparsity algorithm with a synthetically generated dataset and we further apply it to quarterly financial statements from companies in financial, healthcare and IT sectors of the US market. We provide evidence that the counterfactual explanation can capture the nature of the real statement features that changed between the current quarter and the following quarter when ratings improved. The empirical results show that the higher the rating of a company the greater the "effort" required to further improve credit rating.